AIIMS UG 2013 Mock Test

A uniform force of $(3\hat{i}+\hat{j})\text{N}$ acts on a particle of mass $2\text{kg}$. Hence the particle is displaced from position $(2\hat{i}+\hat{k})\text{m}$ to position $(4\hat{i}+3\hat{j}-\hat{k})\text{m}$. The work done by the force on the particle is:

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $1\text{kg}$ moves with a speed of $12\text{m/s}$ and the second part of mass $2\text{kg}$ moves with $8\text{m/s}$ speed. If the third part flies off with $4\text{m/s}$ speed, then its mass is:

A rod $PQ$ of mass $M$ and length $L$ is hinged at end $P$. The rod is kept horizontal by a massless string tied to point $Q$. When the string is cut, the initial angular acceleration of the rod is:

A small object of uniform density rolls up a curved surface with an initial velocity $v$. It reaches up to a maximum height of $\frac{3v^2}{4g}$ with respect to the initial position. The object is a:

A body of mass $m$ is taken from the earth's surface to the height equal to twice the radius ($R$) of the earth. The change in potential energy of the body will be: